Report of the fit

Fit summary

Description: PV19 version x. Initial parameters fluctuated.
Minimiser: minuit
Random seed: 1234
Maximum values allowed for q_T / Q: 0.2
Cut on the error function: 2.5
Parameterisation: PV19x
Explicit formula:

f_{\rm NP}(x,\zeta, b_T)= \Biggl( \frac{1-\lambda}{1 + g_1(x) b_T^2/4} + \lambda \exp \left(-g_{1B}(x) b_T^2 / 4 \right)\Biggr) \exp\left[- g_2 \log\left(\frac{\zeta}{Q_0^2}\right) b_T^2/4 - g_{2B} \log\left(\frac{\zeta}{Q_0^2}\right) b_T^4/4 \right]g_1(x) = \frac{N_1}{x\sigma} \exp\left[ - \frac{\ln^2\left(\frac{x}{\alpha}\right)}{2 \sigma^2} \right]g_{1B}(x) = \frac{N_{1B}}{x\sigma_B} \exp\left[ - \frac{\ln^2\left(\frac{x}{\alpha_B}\right)}{2 \sigma_B^2} \right]Q_0^2 = 1\;{\rm GeV}^2 t_0 prescription: True

g_2 N_1 \alpha \sigma \lambda N_{1B} \alpha_B \sigma_B g_{2B}
0.02351590841248 0.9422997060112 0.2036619541611 0.326688434032 0.6715638120608 0.04591270083373 0.06702302432024 0.4193674275496 0.01624238607691

Theory summary

Collinear PDF set: MMHT2014nnlo68cl member 0
Collinear FF set: DSS14_NLO_PiSum member 0
b^* prescription: bstarmin
Perturbative order: N3LL
Reference value of the fine-structure constant: \alpha(Q = 91.1876\;{\rm GeV}) = 0.00776578395589 (running True)

Global statistical estimators

N_{rep} = 215
\chi_{0}^2 = 1.0347
\chi_{mean}^2 = 1.0409
\langle\chi^2\rangle \pm \sigma_{\chi^2} = 1.0655 \pm 0.0169
\langle E \rangle \pm \sigma_{E} = 2.032 \pm 0.1731

Parameters

Parameter Central replica Average over replicas Fixed
g_2 0.032421552 0.03038564 \pm 0.01165879 False
N_1 0.88029848 1.12441055 \pm 1.28546903 False
\alpha 0.20236078 0.20639491 \pm 0.01379061 False
\sigma 0.31874799 0.32097298 \pm 0.06659915 False
\lambda 0.6758279 0.65726592 \pm 0.09063997 False
N_{1B} 0.041086011 0.04557651 \pm 0.01501846 False
\alpha_B 0.06963174 0.07047502 \pm 0.01026502 False
\sigma_B 0.38573834 0.37008864 \pm 0.11892036 False
g_{2B} 0.014857144 0.01485766 \pm 0.00387668 False
Fitted parameter correlation matrix

Fit properties

Global \chi^2 distribution
Global error function distribution
g_2 distribution
N_1 distribution
\alpha distribution
\sigma distribution
\lambda distribution
N_{1B} distribution
\alpha_B distribution
\sigma_B distribution
g_{2B} distribution

Table of \chi^2’s

Central-replica \chi^2’s:
Experiment Number of points \chi_{D}^2 \chi_{\lambda}^2 \chi^2
E605_Q_7_8 7 0.6409 0.0014 0.6423
E605_Q_8_9 8 1.5475 0.0004 1.5479
E605_Q_10.5_11.5 10 0.4648 0.1565 0.6213
E288_200_Q_4_5 4 0.6701 0.7756 1.4457
E288_200_Q_5_6 5 1.6172 0.2007 1.8179
E288_200_Q_6_7 6 0.367 0.1015 0.4684
E288_200_Q_7_8 7 0.538 0.002 0.54
E288_200_Q_8_9 8 0.5951 0.0477 0.6428
E288_300_Q_4_5 4 0.5335 0.4563 0.9899
E288_300_Q_5_6 5 0.838 0.1068 0.9448
E288_300_Q_6_7 6 0.507 0.0182 0.5252
E288_300_Q_7_8 7 0.1288 0.0069 0.1357
E288_300_Q_8_9 8 0.4834 0.0016 0.485
E288_400_Q_5_6 5 0.2955 0.0002 0.2958
E288_400_Q_6_7 6 0.086 0.0052 0.0912
E288_400_Q_7_8 7 0.0242 0.0291 0.0532
E288_400_Q_8_9 8 0.4447 0.0557 0.5004
E288_400_Q_11_12 11 0.5017 0.0636 0.5653
E288_400_Q_12_13 12 0.4894 0.0552 0.5446
E288_400_Q_13_14 12 0.6029 0.0978 0.7007
STAR_510 7 0.8882 0.0375 0.9257
CDF_RunI 25 0.5319 0.0577 0.5896
CDF_RunII 26 0.8466 0.0027 0.8493
D0_RunI 12 0.597 0.0439 0.6409
D0_RunII 5 0.9087 0.5825 1.4912
D0_RunIImu 3 2.9385 0.0256 2.9641
LHCb_7TeV 7 1.0896 0.1472 1.2368
LHCb_8TeV 7 0.6181 0.1 0.7181
LHCb_13TeV 7 0.8796 0.0262 0.9058
CMS_7TeV 4 2.117 0 2.117
CMS_8TeV 4 1.4011 0.0071 1.4082
ATLAS_7TeV_y_0_1 6 2.5001 0.0276 2.5277
ATLAS_7TeV_y_1_2 6 4.1178 1.0352 5.1529
ATLAS_7TeV_y_2_2.4 6 3.5149 0.3817 3.8966
ATLAS_8TeV_y_0_0.4 6 1.9202 0.3487 2.2689
ATLAS_8TeV_y_0.4_0.8 6 2.1954 0.2606 2.4559
ATLAS_8TeV_y_0.8_1.2 6 0.8627 0.0634 0.9261
ATLAS_8TeV_y_1.2_1.6 6 0.8989 0.104 1.0028
ATLAS_8TeV_y_1.6_2 6 0.5636 0.0738 0.6374
ATLAS_8TeV_y_2_2.4 6 0.6445 0.279 0.9235
ATLAS_8TeV_Q_46_66 4 2.2661 0.7195 2.9856
ATLAS_8TeV_Q_116_150 8 0.4965 0.0032 0.4997
Total 319 - - 1.0347
Mean-replica \chi^2’s:
Experiment Number of points \chi_{D}^2 \chi_{\lambda}^2 \chi^2
E605_Q_7_8 7 0.5534 0.027 0.5804
E605_Q_8_9 8 1.1713 0.0285 1.1998
E605_Q_10.5_11.5 10 0.2253 0.1561 0.3815
E288_200_Q_4_5 4 0.2585 0.4542 0.7127
E288_200_Q_5_6 5 0.9114 0.2126 1.124
E288_200_Q_6_7 6 0.2511 0.1147 0.3659
E288_200_Q_7_8 7 0.5005 0.0132 0.5136
E288_200_Q_8_9 8 0.7986 0.02 0.8186
E288_300_Q_4_5 4 0.2503 0.3456 0.5959
E288_300_Q_5_6 5 0.5547 0.152 0.7067
E288_300_Q_6_7 6 0.4545 0.0487 0.5032
E288_300_Q_7_8 7 0.1387 0.0215 0.1602
E288_300_Q_8_9 8 0.3972 0.0109 0.408
E288_400_Q_5_6 5 0.2878 0.0253 0.3131
E288_400_Q_6_7 6 0.1049 0.0022 0.1071
E288_400_Q_7_8 7 0.0375 0.01 0.0475
E288_400_Q_8_9 8 0.5503 0.0432 0.5935
E288_400_Q_11_12 11 0.6806 0.0687 0.7493
E288_400_Q_12_13 12 0.7923 0.0496 0.8419
E288_400_Q_13_14 12 1.1274 0.0596 1.187
STAR_510 7 0.7653 0.0612 0.8265
CDF_RunI 25 0.4703 0.0594 0.5296
CDF_RunII 26 0.8568 0.0007 0.8575
D0_RunI 12 0.65 0.0402 0.6902
D0_RunII 5 0.8905 0.5827 1.4732
D0_RunIImu 3 2.9186 0.0261 2.9447
LHCb_7TeV 7 1.0259 0.1649 1.1908
LHCb_8TeV 7 0.6459 0.0956 0.7415
LHCb_13TeV 7 0.8563 0.0249 0.8812
CMS_7TeV 4 2.1183 0 2.1183
CMS_8TeV 4 1.4613 0.0051 1.4664
ATLAS_7TeV_y_0_1 6 3.0761 0.0351 3.1112
ATLAS_7TeV_y_1_2 6 4.2003 1.082 5.2823
ATLAS_7TeV_y_2_2.4 6 3.5882 0.3841 3.9722
ATLAS_8TeV_y_0_0.4 6 1.9839 0.3606 2.3445
ATLAS_8TeV_y_0.4_0.8 6 2.0855 0.3273 2.4128
ATLAS_8TeV_y_0.8_1.2 6 1.0573 0.0911 1.1484
ATLAS_8TeV_y_1.2_1.6 6 0.8265 0.096 0.9224
ATLAS_8TeV_y_1.6_2 6 0.6823 0.0118 0.6941
ATLAS_8TeV_y_2_2.4 6 0.5843 0.24 0.8244
ATLAS_8TeV_Q_46_66 4 2.4774 0.6449 3.1223
ATLAS_8TeV_Q_116_150 8 0.4942 0.0026 0.4968
Total 319 - - 1.0409
Average-over-replicas \chi^2’s:
Experiment Number of points \chi_{D}^2 \chi_{\lambda}^2 \chi^2
E605_Q_7_8 7 0.5301 \pm 0.2036 0.1336 \pm 0.1703 0.6637 \pm 0.1119
E605_Q_8_9 8 1.4211 \pm 0.2676 0.0968 \pm 0.1303 1.5179 \pm 0.2384
E605_Q_10.5_11.5 10 0.4292 \pm 0.3032 0.2265 \pm 0.2673 0.6557 \pm 0.1126
E288_200_Q_4_5 4 0.2302 \pm 1.5175 1.2712 \pm 1.4492 1.5013 \pm 0.3342
E288_200_Q_5_6 5 1.3792 \pm 0.7025 0.4833 \pm 0.6399 1.8625 \pm 0.2392
E288_200_Q_6_7 6 0.1591 \pm 0.4359 0.3401 \pm 0.4263 0.4991 \pm 0.1105
E288_200_Q_7_8 7 0.3682 \pm 0.2832 0.1817 \pm 0.2315 0.55 \pm 0.1695
E288_200_Q_8_9 8 0.5094 \pm 0.1565 0.1375 \pm 0.1524 0.647 \pm 0.0852
E288_300_Q_4_5 4 0.2107 \pm 1.1718 0.8513 \pm 1.0855 1.0619 \pm 0.2725
E288_300_Q_5_6 5 0.6533 \pm 0.5022 0.3446 \pm 0.4636 0.9978 \pm 0.1492
E288_300_Q_6_7 6 0.3655 \pm 0.2934 0.1811 \pm 0.2521 0.5466 \pm 0.1418
E288_300_Q_7_8 7 -0.0046 \pm 0.2119 0.154 \pm 0.1983 0.1494 \pm 0.058
E288_300_Q_8_9 8 0.404 \pm 0.1581 0.1061 \pm 0.1451 0.5101 \pm 0.0894
E288_400_Q_5_6 5 0.1473 \pm 0.3078 0.2129 \pm 0.2788 0.3603 \pm 0.1138
E288_400_Q_6_7 6 -0.0051 \pm 0.1924 0.1356 \pm 0.1884 0.1306 \pm 0.0523
E288_400_Q_7_8 7 -0.0436 \pm 0.1961 0.1402 \pm 0.1833 0.0966 \pm 0.077
E288_400_Q_8_9 8 0.3883 \pm 0.2187 0.156 \pm 0.2056 0.5443 \pm 0.113
E288_400_Q_11_12 11 0.4861 \pm 0.2055 0.121 \pm 0.1339 0.6071 \pm 0.1649
E288_400_Q_12_13 12 0.4542 \pm 0.1483 0.1256 \pm 0.1411 0.5798 \pm 0.0504
E288_400_Q_13_14 12 0.5777 \pm 0.1357 0.1356 \pm 0.123 0.7133 \pm 0.0572
STAR_510 7 0.8069 \pm 0.2044 0.1415 \pm 0.2011 0.9484 \pm 0.0579
CDF_RunI 25 0.4989 \pm 0.1137 0.0971 \pm 0.1124 0.5959 \pm 0.0177
CDF_RunII 26 0.8392 \pm 0.0807 0.043 \pm 0.051 0.8822 \pm 0.0613
D0_RunI 12 0.544 \pm 0.1419 0.103 \pm 0.1362 0.647 \pm 0.037
D0_RunII 5 0.7611 \pm 0.7485 0.7627 \pm 0.7308 1.5237 \pm 0.2302
D0_RunIImu 3 2.4048 \pm 0.8891 0.5369 \pm 0.5761 2.9417 \pm 0.6618
LHCb_7TeV 7 0.8998 \pm 0.3477 0.3593 \pm 0.3473 1.2591 \pm 0.0511
LHCb_8TeV 7 0.5211 \pm 0.3402 0.2406 \pm 0.2962 0.7617 \pm 0.1913
LHCb_13TeV 7 0.8459 \pm 0.1969 0.107 \pm 0.151 0.9529 \pm 0.1333
CMS_7TeV 4 2.1221 \pm 0.012 0.0 \pm 0.0 2.1221 \pm 0.012
CMS_8TeV 4 1.341 \pm 0.1187 0.0683 \pm 0.1018 1.4092 \pm 0.058
ATLAS_7TeV_y_0_1 6 2.5017 \pm 0.312 0.0999 \pm 0.1481 2.6016 \pm 0.2743
ATLAS_7TeV_y_1_2 6 4.2127 \pm 0.4745 1.0264 \pm 0.4413 5.2391 \pm 0.1288
ATLAS_7TeV_y_2_2.4 6 3.5284 \pm 0.2071 0.4086 \pm 0.1603 3.937 \pm 0.1314
ATLAS_8TeV_y_0_0.4 6 1.9146 \pm 0.3393 0.3852 \pm 0.2909 2.2998 \pm 0.1527
ATLAS_8TeV_y_0.4_0.8 6 2.1413 \pm 0.329 0.3546 \pm 0.3138 2.4958 \pm 0.1229
ATLAS_8TeV_y_0.8_1.2 6 0.8871 \pm 0.1651 0.1014 \pm 0.1209 0.9886 \pm 0.0991
ATLAS_8TeV_y_1.2_1.6 6 0.8677 \pm 0.2508 0.1659 \pm 0.1836 1.0337 \pm 0.1676
ATLAS_8TeV_y_1.6_2 6 0.6278 \pm 0.3359 0.1395 \pm 0.1784 0.7673 \pm 0.2658
ATLAS_8TeV_y_2_2.4 6 0.6623 \pm 0.4017 0.3339 \pm 0.2603 0.9962 \pm 0.2806
ATLAS_8TeV_Q_46_66 4 2.1045 \pm 0.6727 0.8761 \pm 0.658 2.9806 \pm 0.1231
ATLAS_8TeV_Q_116_150 8 0.4079 \pm 0.1662 0.0979 \pm 0.165 0.5058 \pm 0.0114
Total 319 - - 1.0655 \pm 0.0169

TMDs in k_T space

TMD PDF of the d at Q = 2 GeV and x = 0.001
TMD PDF of the d at Q = 2 GeV and x = 0.01
TMD PDF of the d at Q = 2 GeV and x = 0.1
TMD PDF of the d at Q = 2 GeV and x = 0.5
TMD PDF of the d at Q = 2 GeV and x = 0.9

Data-theory comparison

E605_Q_7_8 data-theory comparison
E605_Q_8_9 data-theory comparison
E605_Q_10.5_11.5 data-theory comparison
E288_200_Q_4_5 data-theory comparison
E288_200_Q_5_6 data-theory comparison
E288_200_Q_6_7 data-theory comparison
E288_200_Q_7_8 data-theory comparison
E288_200_Q_8_9 data-theory comparison
E288_300_Q_4_5 data-theory comparison
E288_300_Q_5_6 data-theory comparison
E288_300_Q_6_7 data-theory comparison
E288_300_Q_7_8 data-theory comparison
E288_300_Q_8_9 data-theory comparison
E288_400_Q_5_6 data-theory comparison
E288_400_Q_6_7 data-theory comparison
E288_400_Q_7_8 data-theory comparison
E288_400_Q_8_9 data-theory comparison
E288_400_Q_11_12 data-theory comparison
E288_400_Q_12_13 data-theory comparison
E288_400_Q_13_14 data-theory comparison
STAR_510 data-theory comparison
CDF_RunI data-theory comparison
CDF_RunII data-theory comparison
D0_RunI data-theory comparison
D0_RunII data-theory comparison
D0_RunIImu data-theory comparison
LHCb_7TeV data-theory comparison
LHCb_8TeV data-theory comparison
LHCb_13TeV data-theory comparison
CMS_7TeV data-theory comparison
CMS_8TeV data-theory comparison
ATLAS_7TeV_y_0_1 data-theory comparison
ATLAS_7TeV_y_1_2 data-theory comparison
ATLAS_7TeV_y_2_2.4 data-theory comparison
ATLAS_8TeV_y_0_0.4 data-theory comparison
ATLAS_8TeV_y_0.4_0.8 data-theory comparison
ATLAS_8TeV_y_0.8_1.2 data-theory comparison
ATLAS_8TeV_y_1.2_1.6 data-theory comparison
ATLAS_8TeV_y_1.6_2 data-theory comparison
ATLAS_8TeV_y_2_2.4 data-theory comparison
ATLAS_8TeV_Q_46_66 data-theory comparison
ATLAS_8TeV_Q_116_150 data-theory comparison